We present the study of 21 continuous GPS (cGPS) stations in Mexico during the time interval that goes from 1 October 2013 to 31 December 2014. The area under investigation produced a slow slip event (SSE) that started in February 2014 and lasted at least until December 2014. Superimposed on this transient signal, the M(w)7.3 Papanoa earthquake struck the region on 18 April 2014 and affected multiple stations. Thanks to an independent component analysis (ICA) technique we are able to separate the postseismic deformation associated with this earthquake from the deformation related to the ongoing SSE. We infer the slip distributions associated with the three tectonically related processes: the coseismic and postseismic slip and the SSE. The inferred postseismic slip distribution reduces the amount of slip related to the SSE in the updip portion of the slab. The moment released by the postseismic processes (afterslip and aftershocks) is estimated to be [8.06 +/- 0.24] x 10(19)Nm, equivalent to [71 +/- 4]% of the moment associated with the main shock. More than 88% of the postseismic moment is released aseismically and the afterslip spatially correlates with the Guerrero seismic gap, suggesting that the region is controlled by stable sliding behavior and rate-strengthening frictional properties.